From Newsgroup: rec.games.backgammon

In another thread "Surprised by XG", I had written:

"I have always argued that cube skill formulas to
"extrapolate cubeful equities and match tables to
"extrapolate "matchful" equities injected systematic
"errors of unknown magnitute, each by itself or both
"in combination. See:

https://groups.google.com/g/rec.games.backgammon/c/GbjfpaiCnUc/m/Hs4LnaF2AQAJ

Reading about plies in rollouts, I came across only
one reference to systematic errors which made me
realise that not only the concept is misunderstood
here in general but my arguments may have been
even more misunderstood or not understood at all
because of my not having expressed myself clearly
enough.

Noo-BG manual v1.00.0, section 8.2 says:

"1. Truncation: instead of rolling out all the way to
"the end of the game, it can stop and pretend its
"evaluation after a few plies is perfect. This may
"obviously introduce some amount of systematic
"error, but in practice this may not matter because:

"3. different positions will be reached in different
"trials, so the correlation between errors in each
"trial weakens and the errors cancel out to some
"extent;

The errors introduced by truncation are "random",
not "systematic". Random errors may "cancel out"
but systematic errors don't. Just because an action,
(i.e. truncation), performed is "consistent", (which is
a quality of systematic error), it doesn't necessarily
produce consistent errors. In fact, the manual does
explicitly acknowledges this fact by saying above:
"different positions will be reached in different trials",
(i.e. the errors introduced will be radomly different).

About extrapolated cubeful equities, by systematic
errors I mean, for example, that the formula fails to
consider "how much play is still left in the game". I
had talked about this in the past, when explaining
how I was making my cube decisions not based on
fancifully calculated equities and winning chances.
My next mutant cube skill experiment I had recently
mentioned will be based on this concept, (i.e. the
various stages of the game with different amounts
of play still left in the game).

About extrapolated "matchful" equities, (I coined it
to mean "match play" and sound like "cubeful"), by
systematic errors I mean, for example, that match
equity tables are "circular", that is they are created
based on equities from games played a certain way,
such as like the bots, then future matchful equities
are calculated using MET's, and then MET's are
further refined using those equities, and so on...

It's simple to know that these systemetic errors do
exists. What's difficult to know if the magnitude of
these errors. Unfortunately, since the past 30+ years
that equity extrapolating formulas and tables have
been used and talked about, these errors have never
been acknowledged, nor has there been any efforts
to quantify their magnitudes, neither has there been
any discussions about mitigating them. :(

Ignorance is bliss. Fallacy is blisser. Dogma is blissest.

MK
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